A sparse matrix typically includes a very large amount of elements (e.g., bytes). Some of these elements include values and are coined “non-zero elements. A large percentage of the elements, however, include zeros (or no values at all), thus, the term “sparse” matrix. Conceptually, sparsity corresponds to systems which are loosely coupled.
A “matrix” may be defined as a two-dimensional array of numerical values. If a preponderance of these values is zero, the matrix may be considered a “sparse matrix.” Conceptually, when a matrix is sparse, the system it represents is “loosely coupled.” Huge sparse matrices often appear in science or engineering when solving partial differential equations. For example, sparse matrices may be used in applications with underlying 2D or 3D geometry (such as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations). Sparse matrices may also be used in applications that typically do not have such geometry (such as optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs).